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@fhuszar
Created December 12, 2013 11:34
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This is an ipython notebook file containing basic analysis of London tech startup using AngelList's API, Laplacian eigenmaps and spectral clustering.
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{
"metadata": {
"name": "AngelList"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": "Analysing The London startup clusters\n-------------------------------------\n\nThis is a little experiment that I ran to visualise the startup ecosystem in London, using tools like Laplacian eigenmaps and spectral clustering. It really demonstrates how easy it is to do basic visualisation and clustering on well-behaved data.\n\nI use [AngelList's fee API](https://angel.co/api) to get some data. Playing with the search functionality I quickly found out that the tag '1695' corresponds to 'London', so most startups which have presence or headquarters in London would have this tag. This is a bit inaccurate, and for example taxi app Hailo is not featured here, but it's good for a demonstration. Below is the very simple code I used to access the API. The only interesting bit is the eventlet module, which allows me to easily make 20 concurrent API calls, speeding the process up significantly."
},
{
"cell_type": "code",
"collapsed": false,
"input": "import simplejson as json\nfrom eventlet import GreenPool\nfrom eventlet.green import urllib2 as urllib2\n\ndef get_page(url):\n return json.loads(urllib2.urlopen(url).read())\nbase_url = 'https://api.angel.co/1/tags/1695/startups'\nresponse = get_page(base_url)\nlast_page = response['last_page']\n\npool = GreenPool(20)\nstartups = []\nfor item in pool.imap(get_page,[base_url+'?page=%d'%(page_num+1) for page_num in range(last_page)]):\n startups.extend(item['startups'])",
"language": "python",
"metadata": {},
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": "I've filtered out startups which are 'hidden', as these don't have any public information available about them. To make the rest of the analysis more meaningful I also get rid of startups which have less than 2 market tags."
},
{
"cell_type": "code",
"collapsed": false,
"input": "non_hidden = filter(lambda(x):not x['hidden'],startups)\nnon_hidden = filter(lambda(x):len(x['markets'])>1,non_hidden)",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 191
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Just checking if the startup I work for, PeerIndex is in the list:"
},
{
"cell_type": "code",
"collapsed": false,
"input": "'PeerIndex' in set([item['name'] for item in non_hidden])",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 193,
"text": "True"
}
],
"prompt_number": 193
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Affinity/similarity calculations\n--------------------------------\n\nI'll base my analysis on market tags. AngelList allows startups to enter multiple tags that describe the markets they are targeting, for example 'mobile commerce', 'e-commerce' or 'social networks'. These are entered by humans, and are therefore a little noisy. Nevertheless I found that this is great signal, and contains a lot of useful information.\n\nThe following snippet of code transforms the json-like objects returned by AngelList API to a sparse matrix. Possibly I could have used a library like scikit-learn's preprocessing module, but I had this code lying around so I could just reuse this."
},
{
"cell_type": "code",
"collapsed": false,
"input": "import numpy as np\nfrom scipy.sparse import coo_matrix\n\ndef sparse_encoding(items):\n dictionary = {}\n maxid = 0\n ii = []\n jj = []\n v = []\n for i,item in enumerate(items):\n for tag in item:\n j = dictionary.setdefault(tag,maxid)\n if j==maxid:\n maxid = maxid+1\n jj.append(j)\n ii.append(i)\n v.append(1)\n \n return coo_matrix((v,(ii,jj))),dictionary",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 77
},
{
"cell_type": "markdown",
"metadata": {},
"source": "The result is a sparse matrix where there's non-zero element at position (i,j) if startup i has the market tag j. There are about 1.7k startups and some 500 market tags in the dataset. Note that that's probably not all startups in London, only ones which have a profile on AngelList with a correct location tag."
},
{
"cell_type": "code",
"collapsed": false,
"input": "data,dictionary = sparse_encoding([set([market['id'] for market in startup['markets']]) for startup in non_hidden])\nspy(data.T)",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 190,
"text": "<matplotlib.lines.Line2D at 0x111ff53d0>"
},
{
"output_type": "display_data",
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59dZbueKKK/jQhz7ExEQcte+++24uv/xyrrzySh566KGemXvIAGP1y+pA1m1L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\nGguP0N8AJuYtyCuqk4QTm0rzV9w0fBNK6jM9+yxNdy5pnwp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+qlG3zt5DH2ZDlodNz8NM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\nChBjLgiCMAWIMRcEQZgC/gdTUoAf8ESINAAAAABJRU5ErkJggg==\n"
}
],
"prompt_number": 190
},
{
"cell_type": "markdown",
"metadata": {},
"source": "To analyse this data I'll compute pairwise affinities between startups. I'll use cosine distance between the binary vectors describing the market tags associated with startups. The code below is a bit inefficient as I convert the sparse matrix to a dense one, but with this much data it didn't make a difference and I couldn't be bothered to use anything more sophisticated. It is possible to compute cosine distances without making your data matrix sparse."
},
{
"cell_type": "code",
"collapsed": false,
"input": "from scipy.spatial.distance import pdist,squareform\nA = 1-squareform(pdist(data.todense(),'cosine'))\nA[isnan(A)] = 0\nspy(A)\nxlabel('startups')\nylabel('startups')\ntitle('similarity between startups')",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 192,
"text": "<matplotlib.text.Text at 0x111b630d0>"
},
{
"output_type": "display_data",
"png": 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el5wyDlMjrWqrQ1eUg3EB0zBbdc+kjQtQ+ITquezduxc33HADAOD06dOYMmUK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\nG5cYMWIEgv8Hac6ldATVTr0AAAAASUVORK5CYII=\n"
}
],
"prompt_number": 192
},
{
"cell_type": "markdown",
"metadata": {},
"source": "The result is a sparse matrix, not much structure is visible, because startups are ordered randomly (well, not randomly, based on number of followers on AngelList, but that's random for the purposes of this analysis). Let us reorder startups cleverly so that more structure becomes visible. I'll perform simple Laplacian eigenmaps: compute the graph laplacian L, and compute it's smallest eigenvectors. The second smallest eigenvector will be a good dimension along which to order startups. for more info on Laplacian eigenmaps, I recommend you read [the original paper](http://www.cse.ohio-state.edu/~mbelkin/papers/LEM_NC_03.pdf)."
},
{
"cell_type": "code",
"collapsed": false,
"input": "from scipy.sparse.linalg import eigsh\nAreg = A + 0.02*ones(A.shape)\nD = diag(sum(Areg,0))\nL = D - Areg\nu,v = eigs(L,3,D,which='SM')",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 112
},
{
"cell_type": "code",
"collapsed": false,
"input": "order = sorted(range(data.shape[0]),key=lambda(x):v[x,1])\nspy(A[order,:][:,order])",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 113,
"text": "<matplotlib.image.AxesImage at 0x14c635ad0>"
},
{
"output_type": "display_data",
"png": 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WDqNSHhGdI7vQnKrlVYJEojNuVh948vP6GMpi8dlOtrq2U1wjrBMKXwFKY4ul\n3d2NMkzMTLVhrQteHKYK6ye7GwJkg1OFCY4NH+6Fap2hXBtWMLPojvAsBd/4aqstlYRufCE0LN9U\n55iRLs+Kg7iEZTK7bMfURZShK2Nx/FinFk3FwDqFkMUNTI436fllWTcu4ltt725kMjaUderhst22\ndzdUNanJruIL3bwCm13IFa7q06nHtk0bS6L5t6pLoWNJAPL/5wZtyaicbpjS9pZErBZMCLli6Xss\ncqiSA5dtRMyLM4RcsfQ9FjlUyYHLTKaixBR8TomsJDJJ4DqQVzYxyNAkuozLkDTNwaqZu5ntuJxD\nWV0hYhKmv4Phg2xJZKTEtKuFoh37zKOtlUS2ItRIYYx0H3rRj860W+Cy8keg+UHP+MZ2jYVeo7rt\nJX8EynsTUxdTLVxGEpFNvaHaqQKqMvNSq1UTlURWiU3KPC+ZiiWvzfxUXkkU4QWLfC5gVyalr53G\n9av2qu0U0c0gdXEv74H01Z4LVOamDGUctbtBa0ediLEsAk1/LrZDX6Pbl6Era8YfKoqxOFe+XQPe\nGhTJEkIxCN8TiU1JiAYxlG9n0g49oTxlZHK8ZoqoLtZ429bZDrjov8zipRWD6D6dNun1KWqjSHTu\nBus1WxNstK/MBxWVoWWW9YdlsRSvi/xYGaLx48lrU2c7EEP/bdxpk+crOkuCvtbEhQmv6m6oHnvx\nyO5GtVC19lxZETJLmZeY5ZNKuRuxt1+2nBk7TN1ZXtxK1WVTCaq7cnFZbdoov+jcjdjJCqLaqLhg\nut/Fjq0lkpVEJpM4tgouK4n/YeoDyhJkbOpxCS8QGnsymGqbJmNt8vCwAn+q9dAB8aaZ3/xHJz+J\n1lDRRWiWZ7XHWte645asknBxumFzL2/iXLRpgsrpS9VQidTzgtAq96mUU0WUkxMK44B/aoFLWT2q\nu4jLHA3e2TR9TRQQkyWHsa7zknFU69Hpn+s6Tdo0rYN10iUaVxsZVE5S8ukGh5RODVLqSzui446Y\nKEjbZCqVNkT3qyrFJkJ34+zZs6jVahgaGmpdm5qaQqPRwMjICEZGRnD37t3Wd5cvX0Z/fz8GBgYw\nNzfXun7v3j0MDQ2hv78fFy5cUO6YDWX4yJn4UF0H9EOpG2eQXdOVJyqIgPfee498+OGHZN++fa1r\nU1NT5Nq1a9vu/fjjj8nw8DDZ2toiy8vLpLe3l3zxxReEEEIOHjxIFhYWCCGEvPzyy+Tu3bvbyktE\nqRQp9SV2DXr1AAAEV0lEQVTjHgDMNVK83vzMW0u6a6x4P/1ZVpfQkjh8+DB27drFUizbrs3MzOD0\n6dPo7OxET08P+vr6sLCwgPX1dWxubmJ0dBQAcObMGdy+fdtYqdlisrPolAPYZiQrak1fo9sKtetU\ncndzgG6038U4FU80WLGi5vXm5+bfonWj8q94P/1ZhtFvXL711lv4/e9/jwMHDuDatWv4yle+ggcP\nHuDQoUOtexqNBtbW1tDZ2YlGo9G6Xq/Xsba2xqx3amqq9XlsbAxjY2Mm4j0HHZxiKTgW9H2q5WR1\nseopXqOPtnjY+Jgq7biOq8QYp9GVh3d/jH1zibaSOH/+PH75y18CAH7xi1/gtddew40bN5wIU1QS\nrlB54IqoRpx9YaLEZEpIVp7VN52+qgTvfIwd63RC5XsVRSqru0jKCgIwyJPo6upqmSrnzp3D4uIi\ngP9aCCsrK637VldX0Wg0UK/Xsbq6+tz1er3uQPTtuDAHeRMuW1CucGXS6sB6gGzcK9Y1Hy6NqiXE\ns7JEMuluLipU1a3TVhLr6+utz++++27r5GNiYgK3bt3C1tYWlpeXsbS0hNHRUezevRs7d+7EwsIC\nCCG4efMmjh8/7q4HBXiLpfjfUO36rovnR6taPLzxcPlwxJY4RFs2rmRSXVsqyilGhO7G6dOn8Ze/\n/AX//ve/8eKLL+LSpUuYn5/HRx99hI6ODrz00kv47W9/CwAYHBzEyZMnMTg4iB07duD69eutwbh+\n/Tp++MMf4j//+Q++/e1v41vf+pb/nv2PMtyNEK6Jb3dDhzKSqYpt+HA36DpMvxeVE12LSZHkZCrN\n9suWM2MHK+Bb/C/AfrWaZRXpxC145YuwAtGs+3wgkj/Zdzd0MT31oIlpB7BFty+y+13XZ1Iv70Es\nfkd/bv5Nuyg6VirPvWHVGxvJKglfC1KG7mTHrFRcHRH6bt+0XZM1YprPIiqrk7NQBskpCR1/MwZE\nwdbUiOmkINRplUn7sZHc/zDY9Hw/pkmLSZZYcTFGusfdvGAvK8ZAuzWyOETMJGdJ6BD7BFXBoggl\no6t2RPW4yA3hxS2qTDJKogoPlC6hF5jJGIYy212Nhage3ne2/aj62kxGSaSgsXmEWmRlBR5jx7Yf\nVR+HZJSELTFr+6ovslgp83SDvh7z+stKIlPKAo35ocg8TzJKwueRWOqU0fcYxtskD8RHMpWJLCFJ\n5gjUdpBdplvn1O1qoDtPrLdITdKyVVyWmCytZCwJW1zmyjcXTkwTndmOiSJ3YUmwPtN1xZSunZUE\nA1eJOjFMcMYdLi1Nn/W7Jhl3wwbX7kF2NzIyqvSqeLYkEFd+wPz8vDtBKk6qYyF7I7T4OYbNJiuJ\nyEj1wTAh1bGIyUpQIbsbHsjuRkZGdjfanNQUREwLNhQu+iwKUFbJ3Yjq5+symUw5iNRANO5GJLoq\nk8lQZHcjk8kIyUoik8kIyUoik8kIyUoik8kIyUoik8kIyUoik8kI+T+4YYB67aLidAAAAABJRU5E\nrkJggg==\n"
}
],
"prompt_number": 113
},
{
"cell_type": "markdown",
"metadata": {},
"source": "So now that the startups are ordered by the second smallest eigenvalue of the Laplacian, a cluster structure becomes clearly visible. Let's look at it in more detail, using the second and third smallest eigenvalues to create a map of startups. In the figure below the x axis is the second, y axis is the third smallest eigenvector of the Laplacian, but the meaning of the coordinates is not really relevant. Each dot represents a startup. Startups that are more similar to each other (in terms of cosine distance between their market tags) will be closer to each other on the plot."
},
{
"cell_type": "code",
"collapsed": false,
"input": "plot(v[:,1],v[:,2],'.')",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 114,
"text": "[<matplotlib.lines.Line2D at 0x14c65d090>]"
},
{
"output_type": "display_data",
"png": 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PVmrexPKogkN1w9a/jFx59a+qKt/OkwkuISlIjh8/LpYtWzb6efPmzWLz5s12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\n"
}
],
"prompt_number": 114
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Clearly, a number of clusters emerge. Let's run clustering on the data and see if it identifies these clusters. I'll use SpectralClustering from the scikit-learn package, it's really simple."
},
{
"cell_type": "code",
"collapsed": false,
"input": "from sklearn.cluster import *\nclustering = SpectralClustering(affinity='precomputed',n_clusters = 7)\nlabels = clustering.fit_predict(Areg)\nscatter(v[:,1],v[:,2],c=labels)",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 167,
"text": "<matplotlib.collections.PathCollection at 0x111e2ea50>"
},
{
"output_type": "display_data",
"png": 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gNBjJTMsCoDCnkKyNWURHR3u03Xr16rF793b69q1Nw4YhPPHEAHbs2IyPj88/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\np6p2Q3BwMDk5OWe1OXbsGOHh4VXbYWFhVQkBz9e/uLiYadOmsXLlSqZ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/Olxhe1lZGS+/\n/PIf/kZq+zd/Plx17+12O/n5+axfv55NmzbRv39/Dh06VBMTq8VV9g8ePJg333yTvn37snDhQh54\n4IG//J+96EJyKdamhIeH06lTJ/z9/QHo2bMnW7durZGQXAr7N27cyKJFixg7diwFBQXodDrMZjOP\nPvroFWH/6Xb9+vXj008/vaBrgv5sT3p6OmFhYX9pc1hYGDabrUbXciG5kPb/ue/HH3/MsmXLWLVq\n1RVj+8GDBzl8+DAtWrSoah8fH8/GjRsv+GfgqnsfFhZGv379AGjbti06nY6TJ09Sp06dK8L+jRs3\nsnLlSgBuu+02hgwZ8tfG1NrjcwEZM2ZMVfTAlClTzukgtNlsIjIyUqSlpYmKioqzHKTn6p+Xlyda\nt24tSktLhc1mE127dhXLli27Yuz/PRMnThSvvPLKBbfdlfbn5+eLuLg48fXXX19wm6uz5zS/dziu\nW7euyuFY28/icrZ/+fLlIiYmRuTm5rrEblfa/ntc6Wx3lf0zZ84Uzz33nBBCiL1794rw8PAryv5W\nrVqJ1NRUIYQQK1euFG3atPlLWy4rITl58qTo0qXLWSGXx44dEz179qxqt2zZMhEdHS2ioqLEyy+/\n/Jf9hRBi7ty5olmzZqJ58+Yueyi40v7TuFJIXGX/iy++KCwWi2jZsmXV60I+4M5lz8yZM8XMmTOr\n2gwbNkxERUWJuLg4sWXLlhpfiytwhf0NGzYU9evXr7rfQ4cOvWJs/z0NGjRwafivK+y3Wq3i7rvv\nFs2bNxetW7cWP/zwwxVl/6ZNm0S7du1EixYtRIcOHf4QMnw+arwgUaFQKBQKuMyithQKhUJx5aGE\nRKFQKBS1QgmJQqFQKGqFEhKFQqFQ1AolJAqFQqGoFUpIFAqFQlEr/ge5U7Xakqn67AAAAABJRU5E\nrkJggg==\n"
}
],
"prompt_number": 167
},
{
"cell_type": "markdown",
"metadata": {},
"source": "When we colour the dots according to the cluster labels spectral clustering found, we see that it roughly identified the clusters that were visible anyway. It does not look perfect, but that's because of the imperfect visualisation of the graph: Laplacian eigenmaps only gives us an approximate look at the structure of the data. Below I list the clusters that spectral clustering found, along with the 3 most popular market tags in each cluster and 10 examples of startups for each."
},
{
"cell_type": "code",
"collapsed": false,
"input": "from collections import Counter\nfor l in range(7):\n cnt = Counter([market['name'] for startup,label in zip(non_hidden,labels) if label==l for market in startup['markets']])\n print 'Cluster %d, (%s)'%(l,', '.join([item[0] for item in cnt.most_common(3)]))\n for name,markets in [(startup['name'],[market['name'] for market in startup['markets']]) for startup,label in zip(non_hidden,labels) if label==l][:10]:\n print '\\t%s:\\t\\t%s'%(name,markets)",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Cluster 0, (SaaS, enterprise software, mobile)\n\tPopcorn Metrics:\t\t['SaaS', 'analytics', 'marketplaces', 'predictive analytics']\n\tNirit:\t\t['SaaS', 'location based services', 'private social networking']\n\tOmetria:\t\t['SaaS', 'e-commerce', 'retail technology', 'big data analytics']\n\tTask Tub:\t\t['SaaS', 'project management']\n\tUCi2i:\t\t['enterprise software', 'collaboration', 'small and medium businesses', 'unifed communications']\n\tCollider13:\t\t['SaaS', 'B2B', 'marketplaces', 'big data']\n\tDeontics :\t\t['SaaS', 'health care', 'big data', 'artificial intelligence']\n\tSlivers-of-Time:\t\t['SaaS', 'ventures for good', 'recruiting', 'human resources']\n\tBeem:\t\t['mobile', 'SaaS', 'enterprise software', 'B2B']\n\tReceipt Bank:\t\t['SaaS', 'accounting', 'document management']\nCluster 1, (education, marketplaces, advertising)\n\tB2BWave:\t\t['B2B', 'wholesale', 'trading']"
},
{
"output_type": "stream",
"stream": "stdout",
"text": "\n\tYumbles:\t\t['food and beverages', 'specialty foods', 'organic food']\n\tAgonyapp:\t\t['q&a', 'women', 'private social networking', 'lifestyle']\n\tEchobox:\t\t['analytics', 'artificial intelligence']\n\tEpicum Films:\t\t['film', 'entertainment industry', 'film distribution']\n\tTrip Cubes:\t\t['publishing', 'hotels', 'social media marketing', 'travel & tourism']\n\tTechspace London:\t\t['startups', 'coworking', 'office space']\n\tVICTORIA SPRUCE:\t\t['fashion', 'product design', 'design', 'shoes']\n\tInspiredChallenge:\t\t['online travel', 'social travel', 'adventure travel', 'travel & tourism']\n\tWeknowvid:\t\t['internet tv', 'video streaming']\nCluster 2, (e-commerce, fashion, marketplaces)\n\tCOS Ventures:\t\t['e-commerce', 'venture capital']\n\tClothfusion:\t\t['e-commerce', 'retail', 'fashion']\n\tRare Pink:\t\t['e-commerce', 'retail', 'jewelry']\n\tBaskettt:\t\t['e-commerce', 'personal finance']\n\tQikd:\t\t['e-commerce', 'retail', 'mobile commerce', 'coupons']\n\tawesome.bi:\t\t['e-commerce', 'consulting', 'retail technology', 'big data analytics']\n\tVirtualOS:\t\t['enterprise software', 'e-commerce', 'virtual workforces', 'office space']\n\tStylect:\t\t['mobile', 'e-commerce', 'fashion', 'mobile commerce']\n\tTeeleap:\t\t['e-commerce', 'retail', 'brand marketing', 'crowdfunding']\n\tWonderLuk:\t\t['e-commerce', 'fashion', '3d printing']\nCluster 3, (mobile, location based services, education)\n\tFeerce:\t\t['mobile', 'location based services', 'messaging']"
},
{
"output_type": "stream",
"stream": "stdout",
"text": "\n\tArtRate:\t\t['mobile', 'art', 'events', 'contests']\n\tAngie Fiber Communications:\t\t['mobile', 'telecommunications', 'wireless', 'optical communications']\n\tSurvey On Tablet Ltd:\t\t['mobile', 'android', 'tablets', 'customer service']\n\tToDone:\t\t['mobile', 'location based services', 'task management']\n\tInstaSpa :\t\t['mobile', 'personal health', 'health and wellness']\n\tOrin:\t\t['mobile', 'music', 'music services', 'musicians']\n\tLowdownapp Ltd:\t\t['mobile', 'B2B']\n\tRedeemia:\t\t['mobile', 'mobile commerce', 'deals', 'discounts']\n\tVeleza:\t\t['mobile', 'reviews and recommendations', 'cosmetics', 'big data analytics']\nCluster 4, (social media, mobile, social commerce)\n\tcardkiwi.com:\t\t['social media', 'education', 'k 12 education']\n\tTAG Education:\t\t['social media', 'clean technology', 'education', 'k 12 education']\n\tFoundbite (by Mendzapp):\t\t['mobile', 'social media', 'photo sharing']\n\tdubble :\t\t['mobile', 'social media', 'photography', 'private social networking']\n\tFootballtracker:\t\t['social media', 'sports', 'soccer']\n\tClipling:\t\t['social media', 'news', 'social bookmarking', 'social news']\n\tSayPublic:\t\t['social media', 'market research']\n\tStyloola:\t\t['social media', 'fashion', 'retail technology']\n\tThe Woo Game:\t\t['social media', 'online dating']\n\tX-Ray:\t\t['social media', 'crowdsourcing', 'browser extensions', 'content discovery']\nCluster 5, (digital media, social media, mobile)\n\tTemple Bright LLP:\t\t['digital media', 'e-commerce', 'startups', 'legal']"
},
{
"output_type": "stream",
"stream": "stdout",
"text": "\n\tPlaything:\t\t['digital media', 'advertising', 'social media platforms', 'user experience design']\n\tSouthern Cloud:\t\t['digital media', 'video', 'video streaming', 'hardware + software']\n\tTeenPoke, Inc.:\t\t['digital media', 'social media', 'teenagers', 'social network media']\n\tBizarre Dragon:\t\t['digital media', 'kids', 'mobile games', 'digital entertainment']\n\tAnimal Vegetable Mineral Limited:\t\t['digital media', 'mobile games', 'social television']\n\tNeotericUK Pvt Ltd:\t\t['digital media', 'e-commerce', 'SEO', 'web design']\n\tExclusive Sports Media Global LTD:\t\t['digital media', 'sports', 'brand marketing', 'social news']\n\tDrivn:\t\t['mobile', 'digital media', 'local', 'quantified self']\n\tLobster :\t\t['digital media', 'social media', 'marketplaces', 'crowdsourcing']\nCluster 6, (financial services, finance technology, finance)\n\tdiliger:\t\t['financial services', 'investment management', 'trading']\n\tRainMaker:\t\t['investment management', 'finance', 'finance technology']\n\tCrowd Mortgage Ltd:\t\t['real estate', 'financial services', 'peer-to-peer']\n\tThe City PA :\t\t['financial services', 'startups']\n\tPaper Street:\t\t['financial services', 'peer-to-peer', 'finance', 'crowdfunding']\n\tKensington & Chelsea Investment Project:\t\t['financial services', 'business development']\n\tchronext.com:\t\t['financial services', 'e-commerce', 'trading', 'curated web']\n\tAlpha R E Investment LLP:\t\t['financial services', 'location based services', 'private social networking', 'angel investing']\n\tProplend | Secured P2P Lending:\t\t['financial services', 'peer-to-peer', 'financial exchanges', 'commercial real estate']\n\tSpace Miles Holdings Ltd:\t\t['financial services', 'adventure travel']\n"
}
],
"prompt_number": 187
},
{
"cell_type": "markdown",
"metadata": {},
"source": "So that's it. It really wasn't hard. In comparison, doing the same thing over twitter users was considerably harder - AngelList data is fairly well behaved."
}
],
"metadata": {}
}
]
}
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